slaed5.c

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/* slaed5.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Subroutine */ int slaed5_(integer *i__, real *d__, real *z__, real *delta, 
        real *rho, real *dlam)
{
    /* System generated locals */
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    real b, c__, w, del, tau, temp;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  This subroutine computes the I-th eigenvalue of a symmetric rank-one */
/*  modification of a 2-by-2 diagonal matrix */

/*             diag( D )  +  RHO *  Z * transpose(Z) . */

/*  The diagonal elements in the array D are assumed to satisfy */

/*             D(i) < D(j)  for  i < j . */

/*  We also assume RHO > 0 and that the Euclidean norm of the vector */
/*  Z is one. */

/*  Arguments */
/*  ========= */

/*  I      (input) INTEGER */
/*         The index of the eigenvalue to be computed.  I = 1 or I = 2. */

/*  D      (input) REAL array, dimension (2) */
/*         The original eigenvalues.  We assume D(1) < D(2). */

/*  Z      (input) REAL array, dimension (2) */
/*         The components of the updating vector. */

/*  DELTA  (output) REAL array, dimension (2) */
/*         The vector DELTA contains the information necessary */
/*         to construct the eigenvectors. */

/*  RHO    (input) REAL */
/*         The scalar in the symmetric updating formula. */

/*  DLAM   (output) REAL */
/*         The computed lambda_I, the I-th updated eigenvalue. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Ren-Cang Li, Computer Science Division, University of California */
/*     at Berkeley, USA */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    --delta;
    --z__;
    --d__;

    /* Function Body */
    del = d__[2] - d__[1];
    if (*i__ == 1) {
        w = *rho * 2.f * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.f;
        if (w > 0.f) {
            b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
            c__ = *rho * z__[1] * z__[1] * del;

/*           B > ZERO, always */

            tau = c__ * 2.f / (b + sqrt((r__1 = b * b - c__ * 4.f, dabs(r__1))
                    ));
            *dlam = d__[1] + tau;
            delta[1] = -z__[1] / tau;
            delta[2] = z__[2] / (del - tau);
        } else {
            b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
            c__ = *rho * z__[2] * z__[2] * del;
            if (b > 0.f) {
                tau = c__ * -2.f / (b + sqrt(b * b + c__ * 4.f));
            } else {
                tau = (b - sqrt(b * b + c__ * 4.f)) / 2.f;
            }
            *dlam = d__[2] + tau;
            delta[1] = -z__[1] / (del + tau);
            delta[2] = -z__[2] / tau;
        }
        temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
        delta[1] /= temp;
        delta[2] /= temp;
    } else {

/*     Now I=2 */

        b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
        c__ = *rho * z__[2] * z__[2] * del;
        if (b > 0.f) {
            tau = (b + sqrt(b * b + c__ * 4.f)) / 2.f;
        } else {
            tau = c__ * 2.f / (-b + sqrt(b * b + c__ * 4.f));
        }
        *dlam = d__[2] + tau;
        delta[1] = -z__[1] / (del + tau);
        delta[2] = -z__[2] / tau;
        temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
        delta[1] /= temp;
        delta[2] /= temp;
    }
    return 0;

/*     End OF SLAED5 */

} /* slaed5_ */